Coplanar waveguide structures loaded with split-ring resonators

COPLANAR WAVEGUIDE STRUCTURES LOADED WITH SPLIT-RING RESONATORS F. Falcone,1 F. Martı́n,2 J. Bonache,2 R. Marqués3 and M. Sorolla1 1 Departamento de Ingenierı́a Eléctrica y Electrónica Universidad Pública de Navarra 31006 Pamplona (Navarra), Spain 2 Departament d’Enginyeria Electrònica Universitat Autònoma de Barcelona 08193 Bellaterra (Barcelona), Spain 3 Departamento de Electrónica y Eletromagnetismo Facultad de Fı́sica Universidad de Sevilla Av. Reina Mercedes s/n 41012 Sevilla, Spain Figure 4 Reflectance and transmittance of the 90° waveguide bend calculated using FDTD and the PC-based PML. The PML thickness used for the input and output waveguides is N⌬z ⫽ 15a, and the PML polynomial index is n ⫽ 2 dramatically reduces reflections from the ABC. The results may also provide a useful guideline to other researchers for selecting 3D PC-based PML parameters. The formulation has been used to analyze a 90° waveguide bend in a 3D layer-by-layer PC. It provides accurate results by practically eliminating unphysical ripples seen in previous transmittance and reflectance calculations. The concepts presented in this paper are expected to apply equally well to other types of 3D PC waveguides. ACKNOWLEDGMENTS This work was supported by an Australian Research Council Discovery Grant and a Macquarie University Research Fellowship. The authors would like to thank the Australian Centre for Advanced Computing and Communications (AC3) for providing access to their supercomputing facilities. Received 21 June 2003 ABSTRACT: Coplanar waveguide (CPW) transmission lines periodically coupled to split-ring resonators (SRRs) are analyzed, designed, and characterized. Due to inductive coupling between the lines and SRRs, signal propagation is inhibited in the vicinity of the resonant frequency of the rings. The result is a stop-band behavior that can be of interest for the elimination of frequency parasitics in CPW-based devices. Two different approaches are envisaged: a uniplanar structure, where CPW and rings share the same metal level; and a bimetal structure with SRRs etched on the back side of the substrate. It has been found that the latter exhibits almost negligible insertion losses in the pass band, and sharp cutoff and a high level of rejection in the stop band, with few unit cells. Since ring dimensions are small compared to the signal wavelength at resonance, the proposed SRR-CPWs are very promising for the design of miniaturized microwave circuits. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 3– 6, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11269 Key words: coplanar waveguide technology; split ring resonators; microwave filters; metamaterials REFERENCES 1. K.M. Ho, C.T. Chan, C.M. Soukoulis, R. Biswas, and M. Sigalas, Photonic band gaps in three dimensions: new layer-by-layer periodic structures, Solid State Commun 89 (1994), 413– 416. 2. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Full threedimensional photonic bandgap crystals at near-infrared wavelengths, Science 289 (2000), 604 – 606. 3. A. Chutinan and S. Noda, Highly confined waveguides and waveguide bends in three-dimensional photonic crystal, Appl Phys Lett 75 (1999), 3739 –3741. 4. A. Chutinan and S. Noda, Design for waveguides in three-dimensional photonic crystals, Jpn J Appl Phys 39 (2000), 2353–2356. 5. M. Bayindir, E. Ozbay, B. Temelkuran, M.M. Sigalas, C.M. Soukoulis, R. Biswas, and K.M. Ho, Guiding, bending and splitting of electromagnetic waves in highly confined photonic crystal waveguides, Phys Rev B 63 (2001), 081107. 6. A. Taflove and S.C. Hagness, Computational electrodynamics: The finite-difference time-domain method, 2nd ed., Artech House, Boston, MA, 2000. 7. J.-P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J Comp Phys 114 (1994), 185–200. 8. A. Mekis, S. Fan, and J.D. Joannopoulos, Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides, IEEE Microwave Guided Wave Lett 9 (1999), 502–504. 9. M. Koshiba, Y. Tsuji, and S. Sasaki, High-performance absorbing boundary conditions for photonic crystal waveguide simulations, IEEE Microwave Wireless Comp Lett 11 (2001), 152–154. © 2004 Wiley Periodicals, Inc. 1. INTRODUCTION Split-ring resonators (SRRs), originally proposed by Pendry [1], have recently attracted much attention in the scientific community. Arranged periodically, they can form an effective medium with a negative magnetic permeability in the vicinity of the resonant frequency, and when they are properly combined with metallic wires [2] or embedded in a metallic waveguide [3], an artificial material (metamaterial) with a negative refraction index (NRI) results. More than 30 years ago, Veselago [4] had already predicted exotic properties for NRI materials, such as reversal of the Snell law, Doppler effect, and Cherenkov radiation. Nevertheless, SRRs can be also of interest in the microwave and millimetrewave community for the development of new devices and circuits with unique properties and reduced dimensions. This stems from the fact that SRRs are high Q particles and electrically small at resonance. However, for the success of SRR-based devices, compatibility with PCB or MMIC fabrication technology is required. This work focuses on the investigation of coplanar waveguide (CPW) structures magnetically coupled to SRRs. The aim is to obtain stop-band behavior (based on this coupling) in the longwavelength regime. As will be shown, the proposed structures are compact, provide a high level of frequency selectivity, and do not add extra area when combined with a functional circuit. Therefore, they are very promising and can be an alternative to electromagnetic bandgaps [5] for the elimination of frequency parasitics or MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 1, January 5 2004 3 Figure 1 Topology of the split-ring resonator and relevant dimensions undesired frequency bands [6] in microwave or millimetre-wave circuits. 2. DESIGN OF SRR-CPW STRUCTURES Let us first focus on the description and operation of SRRs. Their topology essentially consists of two concentric rings with splits etched in opposite sides (Fig. 1). Due to the presence of the splits, the structure behaves as a resonator with a high quality (Q) factor at microwave frequencies. When the rings are excited by an external time-varying magnetic field applied parallel to the ring axis, an electromotive force around the rings is generated, which gives rise to current loops in the rings. Thanks to the splits, these current loops are closed through the gap capacitance between concentric rings, and the structure behaves as an externally driven LC circuit with a resonant frequency that can be easily tuned by ring dimensions (r, c, d). It has been previously demonstrated that a three-dimensional (3D) array of rings properly radiated (that is, with magnetic field polarization parallel to ring axis) is able to inhibit signal propagation in the vicinity of the resonant frequency [2]. This has been interpreted as being due to the properties of the composite medium, which exhibits a high positive/negative magnetic permeability in a narrow frequency band below/above resonance. In order to develop planar stop-band structures for microwave circuits, we have considered the possibility of exciting the rings by means of a CPW. The presence of a non-negligible component of the magnetic field parallel to the ring axis is required. Two possibilities arise: (i) SRRs are placed in the slots, at the same metal level than central strip and ground planes, or (ii) SRRs are etched in the back side of the substrate, underneath the slots. Let us consider the advantages and drawbacks of these possible implementations. In both cases, the structure is planar, but the former requires only a single metal level. On the other hand, wide slots are needed in the uniplanar structure to accommodate the rings. This increases the characteristic impedance of the line to extreme values, and matching networks should be cascaded at the input/output ports. By placing the rings on the back side of the substrate, slots can be narrowed and a 50⍀ line can be easily achieved with reasonable lateral dimensions. Regarding magnetic coupling between the SRRs and CPW, it is expected to be higher for the bimetal implementation, provided that the inner radius of the rings is substantially higher than the slot width. Under these conditions, magnetic field lines penetrate efficiently in the cross-sectional area delimited by SRRs and high magnetic coupling is achieved. The two implementations are depicted in Figure 2. For the bimetal structure [Fig. 2(a)], the lateral dimensions of the CPW structure have been determined by means of a transmission line calculator to obtain a 50⍀ characteristic impedance (the parameters of the Arlon 250-LX-0193-43-11 substrate have been considered: ␧ r ⫽ 2.43, thickness h ⫽ 0.49 mm). For the uniplanar device [Fig. 2(b)], the requirement of slots wider than the external diameter of 4 Figure 2 Layouts of the SRR-CPWs: (a) bimetal structure; (b) uniplanar structure the rings leads to a characteristic impedance of 190⍀, and tapered lines are cascaded to improve matching. Ring dimensions have been determined following those in [7] to provide a resonant frequency for the rings of f o ⫽ 7.7 GHz, that is, c ⫽ d ⫽ 0.2 mm, r ⫽ 1.3 mm. The distance l between adjacent rings is 5 mm. 3. LUMPED ELEMENT MODEL OF THE SRR-CPW At the frequencies of interest (that is, in the vicinity of resonance) the SRR-CPW operates in the long wavelength regime. This means that ␤ l ⬍⬍ 1 (with ␤ the propagation constant for guided waves) and hence the structure can be described by means of a lumped element equivalent circuit (Fig. 3). L and C are the per-section inductance and capacitance of the line, respectively, while the SRRs are modelled as a parallel resonant tank (with inductance L s and capacitance C s ) magnetically coupled to the line through a mutual inductance M. Due to the symmetry of the structure, the magnetic wall concept has been used and the circuit shown in Figure 3 actually corresponds to one-half the basic cell. By obtaining the equivalent impedance of the series branch, the circuit can be simplified and the dispersion relation can be easily obtained: cos共␤l 兲 ⫽ 1 ⫺ LC␻2 ⫹ 2 C/C⬘s , ␻o2 4 1⫺ 2 ␻ 冉 冊 (1) Figure 3 Lumped-element equivalent circuit for the basic cell of the SRR-CPW MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 1, January 5 2004 Figure 4 Dispersion diagram for the SRR-CPW with C⬘s ⫽ L s /(M 2 ␻ 2o ), L⬘s ⫽ C s M 2 ␻ 2o and ␻ 2o ⫽ 1/(L s C s ) ⫽ 1/(L⬘s C⬘s ). Line parameters (L and C) can be determined from a transmission line calculator, L s and C s from the SRR model described in [7] and M can be inferred from the fraction f of the slot area occupied by the rings, according to: M ⫽ L 䡠 f. (2) These circuit elements have been calculated for the structure shown in Figure 2(a). The dispersion relation is depicted in a ␻–␤ diagram in Figure 4. As expected, a narrow frequency gap centered at the resonant frequency of the rings, and due to inductive coupling, is visible. 4. SIMULATIONS AND MEASUREMENTS The frequency responses for the structures shown in Figure 2 have been simulated by means of the commercial software CST Microwave Studio. The results (depicted in Fig. 5) confirm the presence of a stop band in the vicinity of f o . Comparable insertion and return losses have been obtained for both structures in the rejected band. In spite of the wider slots for the uniplanar approach, this result is indicative of comparable coupling levels between CPW and SRRs, probably because L is higher for the structure of Figure 2(b). However, outside the frequency gap the bimetal structure exhibits excellent matching with negligible insertion losses, as compared to the uniplanar approach. Therefore, in spite of the two metal levels required, the CPW with SRRs etched on the back side of the substrate is the preferred implementation. Moreover, significant layout area is saved because the host CPW is a 50⍀ line and no matching networks are needed (see Fig. 2). The slight shift in the forbidden bands visible in Figure 5(a) and (b) is thought to be related to the proximity between the host CPW and rings, which can affect L s or C s in a different way. The bimetal structure has been fabricated by means of a standard photo/mask etching technique. The measured frequency response, obtained by means of an HP-8722ES vector network analyzer, and depicted in Figure 6, is in reasonable agreement with the simulation. It is remarkable the measured rejection level in the forbidden band, which is close to 40 dB with only four SRR stages. To gain more insight regarding the reflection properties of these structures, we have used the CST Microwave Studio tool to obtain the currents induced in the rings at resonance (Fig. 7). These currents decrease with the distance to the input port, as expected by virtue of the decaying power level at resonance. As can be seen, the currents induced in the third SRR pair are already very small. Figure 5 Simulated insertion (bold line) and return (thin line) losses for the structures of Fig. 2: (a) bimetal structure; (b) uniplanar structure This result suggests that two ring stages can be enough to produce significant rejection in the vicinity of resonance. The simulation of the bimetal structure with two elemental cells (Fig. 8) indicates a rejection level of 30 dB in the forbidden band. Therefore, the dimensions of the structure can be further optimized by roughly preserving the level of suppression. However, the frequency selectivity is slightly better for the four-stage device, especially for the upper side of the band gap, as inferred from the sharper transition. Nevertheless, it is clear that SRRs provide an effective way to eliminate frequency parasitics in CPW structures. Compared to electromagnetic bandgaps (EBGs), whose reflection properties are based on the Bragg effect, SRRs are electrically small Figure 6 Measured insertion and return losses for the SRR-CPW with rings etched on the back substrate side. For comparison, the simulation results (thin line) are also included MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 1, January 5 2004 5 ACKNOWLEDGMENTS This work has been supported by DGES and CICYT by project contracts, BFM2001-2001, TIC2002-04528-C02-01, and TIC2001-3163. The authors are also indebted to R. Pineda (Omicron Circuits s.l.) for the fabrication of the prototype. REFERENCES Figure 7 Magnitude of the currents induced in the rings at resonance ( f o ⫽ 7.7 GHz) and require few periods to provide significant attenuation in the forbidden band. 5. CONCLUSION In conclusion, it has been found that by magnetically coupling SRR particles to CPWs, stop-band behavior is obtained. This has been interpreted as being due to the high positive/negative magnetic permeability of the composite medium in the vicinity of resonance, and has been corroborated within the framework of the structure’s lumped-element equivalent circuit. Two approaches have been considered: the bimetal device, where SRR are placed underneath the slots on the back side of the substrate; and the uniplanar structure, where SRRs are etched in the upper metal level between central strip and ground planes. It has been found that the former structure exhibits lower insertion losses in the pass band and does not require matching networks. A fabricated fourstage prototype device has demonstrated efficient rejection (⬇40 dB) in the forbidden band, negligible insertion losses in the pass band, and very sharp cutoff. It has been also found that the suppression level is not substantially altered by using only two SRR stages, but at the expense of lower frequency selectivity. The proposed structures can be a very promising alternative to EBGs for the elimination of frequency parasitics and undesired bands in microwave and millimeter-wave devices. 1. J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans Microwave Theory Tech 47 (1999), 2075. 2. D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys Rev Lett 84 (2000), 4184. 3. R. Marqués, J. Martel, F. Mesa, and F. Medina, Phys Rev Lett 89 (2002), 183901. 4. V.G. Veselago, The electrodynamics of substances with simultaneously negative values of ␧ and ␮, Sov Phys Usp 10 (1968), 509. 5. V. Radistic, Y. Qian, R. Coccioli, and T. Itoh, Novel 2D photonic bandgap structure for microstrip lines, IEEE Microwave Guided Wave Lett (1998), 69 –71. 6. T. Lopetegi, M.A.G. Laso, J. Hernández, M. Bacaicoa, D. Benito, M.J. Garde, M. Sorolla, and M. Guglielmi, New microstrip wiggly-line filtres with spurious passband supresión, IEEE Trans Microwave Theory Tech 49 (2001), 1593–1598. 7. R. Marqués, F. Mesa, J. Martel, and F. Medina, Comparative analysis of edge and broadside couple split ring resonators for metamaterial design: Theory and experiment, IEEE Trans Ant Propagat (submitted). © 2004 Wiley Periodicals, Inc. NEW MICROMACHINED MICROSTRIP TRANSMISSION LINES FOR APPLICATION IN MILLIMETER-WAVE CIRCUITS Han-Shin Lee, Sung-Chan Kim, Byoung-Ok Lim, Kyoung-Man Kim, Won-Young Uhm, Young-Hoon Chun, Dong-Hoon Shin, Soon-Koo Kim, Hyun-Chang Park, and Jin-Koo Rhee Millimeter-wave Innovation Technology Research Center (MINT) Dongguk University Pildong 3Ga 26, Joong-Gu Seoul 100-715, Korea Received 10 June 2001 ABSTRACT: In this paper, we describe a new GaAs-based micromachined microstrip line, supported by an electrically supported air-gapped microstrip line (DAML) structure and developed using RF MEMS techniques to achieve low losses at millimeter-wave frequency bands with wide impedance ranges. The measured DAML with a 10-␮m post height shows less than 1.5-dB/cm attenuation at 50 GHz with 20 –100⍀, which agrees well with the simulated results. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 6 –9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11270 Key words: RF MEMS; surface micromachining; microstrip line; airbridge; DAML 1. INTRODUCTION Figure 8 Simulated insertion (bold line) and return (thin line) losses for the bimetal SRR-CPW with two ring stages 6 Recent progress in semiconductor process technology has driven the development of planar monolithic microwave integrated circuits (MMICs), in which the design of a small RF circuit that integrates many functions on a chip while providing high performance is possible. The development of MMICs has increased the MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 40, No. 1, January 5 2004